Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 80


$\color{blue}{\left\{-416, 16\right\}}$

Work Step by Step

The numerator of the rational exponent is even so raising both sides to $\frac{5}{2}$ will not work. Raise both sides to the 3rd power to obtain: $((x+200)^{2/3})^3=36^3 \\(x+200)^2=46,656$ Take the square root of both sides to obtain: $\sqrt{(x+200)^2}=\pm \sqrt{46,656} \\x+200 = \pm \sqrt{216^2} \\x+200 = \pm 216$ Add $-200$ to both sides of the equation to obtain: $\\x=-200 \pm 216 \\x_1=-200-216=-416 \\x_2=-200+216=16$ Upon checking both proposed solutions satisfy the original equation. Thus, the solutions set is $\color{blue}{\left\{-416, 16\right\}}$.
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